Flexural–flexural–extensional–torsional vibration analysis of composite spinning shafts with geometrical nonlinearity

Nezhad, H. Shaban Ali; Hosseini, S.A.A.; Zamanian, M.

doi:10.1007/s11071-017-3479-0

Cited by 15 publications

(23 citation statements)

References 30 publications

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“…These are necessary for obtaining the kinetic and potential energies. References [] give a complete description. In the cylindrical coordinate, stress‐strain relation for an arbitrary orthotropic layer with the fiber orientation η (Figure ) is

\{\begin{matrix} left σ_{x x} \\ left σ_{θ θ} \\ left σ_{r r} \\ left τ_{r θ} \\ left τ_{x r} \\ left τ_{x θ} \end{matrix}\} = [\begin{matrix} {\bar{Q}}_{11} & {\bar{Q}}_{12} & {\bar{Q}}_{13} & 0 & 0 & {\bar{Q}}_{16} \\ {\bar{Q}}_{12} & {\bar{Q}}_{22} & {\bar{Q}}_{23} & 0 & 0 & {\bar{Q}}_{26} \\ {\bar{Q}}_{13} & {\bar{Q}}_{23} & {\bar{Q}}_{33} & 0 & 0 & {\bar{Q}}_{36} \\ 0 & 0 & 0 & {\bar{Q}}_{44} & {\bar{Q}}_{45} & 0 \\ 0 & 0 & 0 & {\bar{Q}}_{45} & {\bar{Q}}_{55} & 0 \\ {\bar{Q}}_{16} & {\bar{Q}}_{26} & {\bar{Q}}_{36} & 0 & 0 & {\bar{Q}}_{66} \end{matrix}] \{\begin{matrix} left ε_{x x} \\ left ε_{θ θ} \\ left ε_{r r} \\ left γ_{r θ} \\ left γ_{x r} \\ left γ_{x θ} \end{matrix}\}

or in compact form

\{σ\} = \{\overset{Q}{true}\} \{ε\}

…”

Section: Equations Of Motion Of a Nonlinear Composite Shaftmentioning

confidence: 99%

“…Kinetic energy computed by the use of Equation considers the variable speed of the shaft and nonlinearity of the eccentricity. If spin speed becomes constant and nonlinear terms of eccentricity is vanished, the expression developed in reference [] is obtained. If eccentricity is large, and nonlinear terms of eccentricity is not negligible, the result is different from one presented in [].…”

Section: Equations Of Motion Of a Nonlinear Composite Shaftmentioning

confidence: 99%

“…If spin speed becomes constant and nonlinear terms of eccentricity is vanished, the expression developed in reference [] is obtained. If eccentricity is large, and nonlinear terms of eccentricity is not negligible, the result is different from one presented in []. In earlier works, the account of eccentricity was inconsistent and the kinetic energy results were accurate only in small eccentricity.…”

Section: Equations Of Motion Of a Nonlinear Composite Shaftmentioning

confidence: 99%

“…Ren et al investigated primary resonances of a composite nonlinear shaft using thin‐walled beam theory. Nezhad et al analyzed the primary resonances of a composite rotating shaft with the application of multiple scales method.…”

Section: Introductionmentioning

confidence: 99%

“…The above review reveals the fact that, nonlinear dynamics of composite shafts have not yet considered in non‐stationary case. In one of the recent investigations, a nonlinear composite shaft was studied with constant speed. So, the dynamic analysis of stationary cases was merely possible.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic analysis of nonlinear rotating composite shafts excited by non‐ideal energy source

Kafi

Hosseini

2019

Z Angew Math Mech

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In this article, nonlinear nonstationary vibration of a rotating composite shaft passing through critical speed excited by non-ideal energy source is investigated. Geometrical nonlinearity, gyroscopic effect, rotary inertia and coupling due to material anisotropy are considered, while shear deformation is neglected. By using Hamilton principle, axial-flexural-flexural-torsional-rotational equations of motion for a composite shaft with variable rotational speed are derived. External source is assumed as non-ideal that causes the interaction between external torque and vibrating system.To obtain the approximate analytical solution, perturbation theory (multiple scales method) is applied to reduce the equations in the neighborhood of the first critical speed. Although, the analysis is done for the first critical speed, one-mode discretization is not enough. Indeed, at least two modes is required to obtain accurate results.The effects of external damping, eccentricity, angle of fibers, resistive torque, nonlinear terms, and also the effect of the extensional-torsional coupling on occurrence of Sommerfeld effect are investigated. It is shown that nonlinearity and coupling possess significant effect on the prediction of Sommerfeld phenomenon. Moreover, as observed, with appropriate implementation of layup and stacking sequence, one can obtain the best performance for the nonstationary behavior of composite shaft. K E Y W O R D Scomposite rotor, multiple-scales method, non-ideal source, nonstationary motion, sommerfeld effect

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\{\begin{matrix} left σ_{x x} \\ left σ_{θ θ} \\ left σ_{r r} \\ left τ_{r θ} \\ left τ_{x r} \\ left τ_{x θ} \end{matrix}\} = [\begin{matrix} {\bar{Q}}_{11} & {\bar{Q}}_{12} & {\bar{Q}}_{13} & 0 & 0 & {\bar{Q}}_{16} \\ {\bar{Q}}_{12} & {\bar{Q}}_{22} & {\bar{Q}}_{23} & 0 & 0 & {\bar{Q}}_{26} \\ {\bar{Q}}_{13} & {\bar{Q}}_{23} & {\bar{Q}}_{33} & 0 & 0 & {\bar{Q}}_{36} \\ 0 & 0 & 0 & {\bar{Q}}_{44} & {\bar{Q}}_{45} & 0 \\ 0 & 0 & 0 & {\bar{Q}}_{45} & {\bar{Q}}_{55} & 0 \\ {\bar{Q}}_{16} & {\bar{Q}}_{26} & {\bar{Q}}_{36} & 0 & 0 & {\bar{Q}}_{66} \end{matrix}] \{\begin{matrix} left ε_{x x} \\ left ε_{θ θ} \\ left ε_{r r} \\ left γ_{r θ} \\ left γ_{x r} \\ left γ_{x θ} \end{matrix}\}

or in compact form

\{σ\} = \{\overset{Q}{true}\} \{ε\}

…”

Section: Equations Of Motion Of a Nonlinear Composite Shaftmentioning

confidence: 99%

Section: Equations Of Motion Of a Nonlinear Composite Shaftmentioning

confidence: 99%

Section: Equations Of Motion Of a Nonlinear Composite Shaftmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Dynamic analysis of nonlinear rotating composite shafts excited by non‐ideal energy source

Kafi

Hosseini

2019

Z Angew Math Mech

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Formulation and free vibration analysis of spinning Timoshenko composite beams using nonlinear geometrically exact theory

Beiranvand,

Hosseini

2024

Z Angew Math Mech

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In this study, a set of generalized nonlinear equations of motion for Timoshenko composite shafts is derived using the geometrically exact approach. These partial differential equations of motion are discretized by Galerkin method and the free vibration of an orthotropic spinning shaft with hinged‐hinged boundary conditions is investigated using the multiple‐scale method. We find that in the case of two mode discretization, composite couplings can have significant linear and nonlinear effects on the behavior of the shaft and that these effects were not predictable in the classical model. Also, in the investigating of composite layering we find that the effects of the fibers angle as well as the composite couplings can be noticeable, and these effects are greater in the case of the asymmetrical layering.

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Forced oscillations and stability analysis of a nonlinear micro-rotating shaft incorporating a non-classical theory

2018

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Flexural–flexural–extensional–torsional vibration analysis of composite spinning shafts with geometrical nonlinearity

Cited by 15 publications

References 30 publications

Dynamic analysis of nonlinear rotating composite shafts excited by non‐ideal energy source

Dynamic analysis of nonlinear rotating composite shafts excited by non‐ideal energy source

Formulation and free vibration analysis of spinning Timoshenko composite beams using nonlinear geometrically exact theory

Forced oscillations and stability analysis of a nonlinear micro-rotating shaft incorporating a non-classical theory

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